Page NEW YORK CITY COLLEGE OF TECHNOLOGY of the City University of New York R DEPARTMENT OF MATHEMATICS Revised Spring 0 W. Colucci, D. DeSantis, and P. Deraney. Updated Fall 0 S. Singh MAT06 and MAT06 FINAL EXAM REVIEW FORM R I. Signed Number Evaluation: Evaluate:. (9) (7)( ) 8. ( ).. ( ) 6. 9 6() 7 (). 7. ( 6) (0) II. Numerical Evaluation: Evaluate each epression when =, y =, and z = : 8. y 9. 7 y z 0. y y. y y III. Formula Substitution: Evaluate the following epressions:. If C (F ), find C when F =. If 9 m and v, findk for k mv. If d 0 and t, then find V for IV. Function Notation d V t Given the functions: f() and g(). Find the following values:. f (0) 6. f( ) 7. f () 8. g () 9. g( ) V. Multiplication of Terms and Powers: y 7df d ef e f y 0.... ( ) ( y) VI. Division of Terms: Reduce:. a b a b. q rs 6qs mn 6. mn r s t 7. 0r s 8. 0 y y 7 z z
Page VII. The Distributive Law: 9. 7( ) 0. y (y y ). r s(r R s 9) Divide: 8y y. y. m m m m. r s r s t 8r s 7r s VIII. Combined Operations: Rewrite and simplify:. Subtract 6 from 6. Subtract a a from a a 7. Subtract 6 from Multiply and Combine: 8. rs(rs) r s 9. 7q (q q) 8r(rs ) 0. (a b b) (ab b). (7 ) ( ). ( 7) 9. ( 6) ( ) IX. Multiplication of Polynomials:. ( 7)( ). ( y 7) 6. ( y )(y ) 7. ( m 7)(m 7) 8. ( )( ) 9. ( )( ) 0. ( )( ) X. Factoring: (Greatest Common Factor, Trinomial, Difference of Squares, and Combined) Factor Completely:. z 8z. b 6by bz. a y 8a y a. y y 6. 6. a 6 7. 9 8. 9. c c 0 60. y 6y 0y 6. 6. 6 6. 6 6. 8
Page R XI. Reducing Fractions: Factor and Reduce: 6. a 8a 6 66. 67. a a b b 8 b 8 XII.Multiplication of Fractions : 68. r s t 8t rs 8 t y 70. 9y 0t 69. 7. a b 6ab b y wz 9w z 8y y wz XIII. Division of Fractions : Divide: a b a b 9 y 7. 7. ay 7. y y ab a a 7. 6 y b c y XIV. Addition and Subtraction of Fractions: Combine: 76. y y 8 8 77. 78. y y 79. 6y 6 XV. Radicals: Simplify: J_ J J _J _J J _J _J _J -~t _J _J J ~t _J _J_J ~t 80. 8. 6 b 9 6a 9a 8. w 8w 8. 8y y 8. 6 8. 86. Add or subtract the following: Multiply or Divide and simplify completely: 7 a b 7b 6a 87. 7 7 88. 89. 0 90. 8 8 9. ( 7) 9. ( )( 6) 9. ( 6)( ) 9. b 9 b 8( ) 9. 96. 0 97. 8 98. 6 0 99.
Page XVI. One Variable First Degree or Linear Equations: Solve and Check: 00. 6a a a 0. 8 t t 6 t 0. R h (h ) 7 (h ) 0. 6z 7z 0 z 0. 0 7 k k 0. y (y 8) ( y) 0 XVII. Fractional Equations: Solve: 8d 7 9 06. 6 07. 08. y 6 8 y 09. y y y 0. XVIII. Decimal Equations: Solve:......w... 0 0.... 6y 0..9. 0.. 0. 6. 0.. 0. 0. XIX. Linear Inequalities Solve the following inequalities and sketch the solution on a number line: 7. 8. 8 9. 6 7 0. ( ) 7 XX. Literal Equations and Formula Rearrangement: Solve each equation for the indicated variable:. Solve for y: y. Solve for p : pv pv mv. Solve for g: V K gt. Solve for m: F r XXI. Quadratic Equations: Solve and Check:. m m 0 6. 0 7. p 0p 0 8. y y 9. 9z 0 0. 9 8
Page R XXII. Checking a solution: Check if the number in parenthesis is a solution to the given equations:. ( = ) ( ) 0. ( = -). ( = 6) 8 7 ( ). ( = -) XXIII. Systems of Two Variable Linear Equations: Solve Graphically:. y y Solve Algebraically: 8. y y 6. 9. y 7 y y 7y 7. 0. 7 y 8 0 y 7 y y 9 0 XXIV. Translating Epressions: Translate into an algebraic epression using a variable:. less than twice an unknown number.. the price of pants at $ and y shirts at $. times a number increased by 7. times the difference of a number and XXV. Word Problems: Show all work and answers:. If twice an unknown number is added to thirteen, the sum is twenty-five. Write an equation that epresses the relationship in this sentence and find the unknown number. 6. When three times an unknown number is subtracted from 0, the result is the unknown number. Write an equation that epresses the relationship in this sentence and find the unknown number. 7. If five times a number is subtracted from, the result is equal to twice the number increased by nine. Write an equation that epresses the relationship in this sentence and find the unknown number. 8. A $00 TV is on sale for % off. What is the sale price? 9. Perl buys a new car, with a down payment of % of the price of the car. The down payment is $0. What is the original price of the car? 0. John can travel 00 miles in five hours. How long will it take him to travel 0 miles?. A plane has a cruising range of 900 miles on its main fuel tank, which holds 0 gallons of fuel. At this rate, how many gallons of fuel would be used in a flight of miles?. The average pass rate in a class of students is 0 students. How many students will pass in a class of 98 students?. Jack can fly at 0 mph in his small plane. If a trip to Ohio takes him ½ hours, how many miles was the trip?
Page 6 R XXVI. Slope and Lines Write each line in slope-intercept form, state the slope, the y-intercept and then sketch the graph.. y. y 6. y 7. y 0 XXVII. Scientific Notation Perform each operation: 8. 0 0 8. 9 0 6. 0 9. 6 0. 0 60.. 0 0.6 0 0 0 6. 6 7 8 0 0 6. 7. 0 0.8 0. 0 6. 9 6 8 0 0.0 0 XXVIII. Pythagorean Theorem: Solve for the indicated sides by using the Pythagorean Theorem: a c b 6. In the right triangle, if a = 6 and b = 8, find c. 6. In the right triangle, if c = and b =, find a. 66. In the right triangle, if a = 6 and b = 6, find c. 67. In the right triangle, if c = 8 and a =, find b.
Page 7 R ANSWERS TO MA06 AND MA06 FINAL EXAM REVIEW - FORM R... 6.. 8 6. 9 7. 8. 9 9. 0.. 9. C. K. V. 6. 7. 8 8. 9. 0. y. d e f. 6 y. 8 y. b. q r t 6. 7. r 0 z 8. 9. 8 0. y 0y 8y y. r s 0r s r s. y y. m m. s t rs. 6. a 7a 7. 8 8 8. 0r s 9. q 0. a b b ab. 6. + 0... y y 9 6. 6y y 0 7. m 9 8. 6 9. 7 6 0. 6 8. z(z ). b( y z). 6a (y y ) OR 6a ( y y ). ( y 6)(y ). ( 8)( ) 6. ( a)( a) 7. ( 7 )(7 ) 8. ( )( ) 9. (c )(c ) 60. y( 7)( ) 6. ( )( ) 6. ( )( ) 6. ( 6 )( ) 6. ( )( ) 6. 66. 67. b 9 b 68. 9rt 69. 9a b 70. a a t 7. w y 7. 7. 9b 6a by 7. c b 7. 76. 9y 8 77. 6y 78. 9y 6y 8 79. 6 80. 8. 8a 9 b
Page 8 R 8. 8w w 8. b 6 8. 8. 0y y 86. 70a b ab E E e. ) e ~ J _J J _t _t _t _t 87. 7 88. 89. 90. 9. 0 7 9. 6 9. 9. 6 6 9. 7 96. 97. 6 98. 0 99. 00. a = 0. t = 0. h = 0. z = 8 0. k = 0. y 06. d 0 7 07. 08. y or 09. y 0... w 6. 9. y. 6. 8 7. 8. 9. 0. - - - 0 - - - - 0-6 - - - - - 0 - - - - 0 6 pv V k. y. p. g. v t Fr m v. m, m 6. 6, 7. p 0, p 8. y 0, y 9. z,z 0. 7 7,. No, since 0. Yes, since 9 9 6 6. Yes, since 9 9. No, since., y 6., y 7., y 8., y 9., y 0., y.. y. 7. ( )., 6 6. 0, 7. 9, 8. $00 9. $,000 0. 9 hours. gallons. 8 students. 90 miles
~ Page 9. y slope: y-intercept: ( 0, ). y slope: 6. y "' ~ "' - " "- ['.._ " - L" I').. ['.._,., - I'- ['.._ -? - 0 ~ - "' I'-,,..._., - slope: I y-intercept: 0, ) R y-intercept: ( 0, ) ( 7. y slope: y-intercept: ( 0, ) J ' "-JI..._,,..._ -. -......_ ' 0 l ' ' ' l's I"-!'-... ' ["-, K 8.. 0 6 9. 0 60. 8 8 0 6. 0 6. 60 6..60 6. 0 6. 66. 6 67.